You press the button once and it uses Dragon Sight on "someone" without you having to change targets. Who "someone" is will be the first person down the list that is a party member and in range.
If you want to use it on a specific target, put your mouse over their name in the party list. It will first check to see if your mouse is over someone. If it is, it will Eye that person.
If you don't have a mouseover, it will check your hard target. This will probably be an enemy, so this line will usually get skipped (since the main point of this macro is to be able to use it on a relevant target without detargeting the enemy).
<c> is companion, for when soloing.
If you have your party list set to default sorting, <6><7><8> in a 2/2/4 party will be the other DDs, prioritizing melee DDs over ranged. <5> is also a DD in a 1/2/5 party. <4> is the other DD in a light party.
If you want, you can also add <2> and <3> at the end. This covers the scenarios where all the DDs are ranged and too far away to benefit from Dragon Sight, so you'll Eye a tank instead.
It doesn't perfectly predict who the best person to Eye is every time, however it's reasonably effective and allows you to Eye an "effective enough" target without changing targets or having to spend the time picking a target yourself.